I unschooled myself a lot without ever knowing it.
Computer Programming. I started out simple and then went complex moving up to VB enterprise
Computer programming is all Algebra, some geometry and some trig. So as you write programs and learn you automatically pick up the usage of math.
Drawing a circle manually requires using SINE and COSINE and RADIUS moving from pixel to pixel.
When I was designing a word processing program I had to develop my own methods of keeping track of data and doing things.
The process of justification, for example, is declaring a fixed length (margin), counting how many places each letter and space is, determining how much room is left and then when you reach the end you're holding the word in a QUE and when you go past your maximum character point that word is held in a variable, a routine is activiated that counts how many spaces were left and then it re-writes the line adding additional spaces to buffer the words and make the right flush.
Then it drops to the next line and dumps the word from the QUE onto that line.
It's all done with math.
In the process of learning you read other peoples code. I came across a dithering program for converting a raw file to a JPEG and it was all math.
Little by little you learn how it works.
As for English I wanted to be an author since I was 7 and I kept at it. I wrote, I re-wrote.
A professional secretary helped me out. She found three major flaws in my writing process.
1). I was writing for me and not for her
2). I wrote in short hand, filling in the blanks with my own mind. I had author's incompleteness in which I'd write abstracts by my own mind knew what was supposed to be there so I never notice how incomplete the line was.
3). I had not idea how to use a comma, so she told don't use it at all.
LEarning to write for YOU and not for ME was the easiest part. I simply treated you like you were a first grader and I explained things at that level instead of the college level for which I was writing.
In other words if I were to write about making a word processor I'd have to spend one whole article just on that justification routine and break it down into the smallest parts so any mind can understand it.
The Abstract part was the most difficult and my way out was to get a SPEECH sytheiserzer program that worked with Word and I'd let the computer READ back my writing to me. I'd find all my grammar errors and I'd hear senetences that were akward and incomplete.
I'd then re-write on the spot.
Doing all of this got me into print more often than previously.
Computer programming also helps with English to a degree, for it teaches you style discipline. You have to form your progam in proper synatx and grammar in order to have it work
That also taught me how to next math and simplify problems.
My justification algorithm started off as five separate sub-routines and after I thought about what I was doing I turned it into one big nested algebraic sub routine that was just line long for the actuall process of justification.
WRiting non-fiction also provide a background in English, Science and History.
I'm working on a book on video right now and I wanted to show how the whole process evolved from the discovery of Amber, Static Electricity and glass making.
In the process of evolving how Television, Motion Pictures and Video came about I had to touch on just about every major Science dude in the world, for they all contributed to the process.
So I have a historly lession that runs like JAmes Burke's "Connections" on PBS going from Acient Greece and China to France, England, America that shows how each component of electronics came from other discoveries.
The Leyden Jar (capacitor) was connected to the rubbed Amber to store a charge for later use.
How the chemical battery came about.
How magnetic field effect turns a compass needle that leads to the concept of coils and wires for transformers.
How Edison accidentally invented the Diode and didn't know what he had so he sold it along with all his DC patents to Tesla who promptly used that diode to make a radio.
How Tesla started the AC electricity we use.
How Edison synchronized his phono machine with his movie camera to make the first music videos in 1893.
All this moved right up to the modern computer and computer based Video work.
It was a huge amount of research and then I had to string it together chronologically and make it fun to read.
I liked the way Burke did his show so I thought along those lines.
Like when I described the man who helped to make modern electronics possible with his discover of nothing.
This man discovered that if he took two halves of a globe and sucked all the air out so there was nothing inside it made a very tight bond.
Well this discovery of nothing proved to be something for Edison when he was trying to make the electric light bulb.
And of course in one of his attempts he made the first diode tube (or valve if you're from England), but since Edison never learned Ohms law he didn't know what he had and he sold it to Tesla who quickly found out what he had!
Now, I've just told you how you can loose out on millions of dollars if you don't something as simple as OHMS law.
I=V/R
Simple algebra
OR
V=I*R
Wherer I is the current in Ampere, V is the voltage and R is the Resistance and you work from the concept
1 Volt = 1 Amp times 1 Ohm of resistance
Now you're learning MATH, HISTORY, SCIENCE and ENGLISH all in one package.
This is how unschooling works
You set out to give a background for the 1st grader in how modern technology came into being and you bring them up to college level.
In the process you and they, learn some names, some time periods in history, some locations around the world, some scientific discoveries, some devices that ended up making your computer and TV set work.
And it all started with an Amber Ball and some Silk Cloth, long, long ago....